Equations over finite fields: Zeta function and Weil conjectures
This work is a review of the congruent zeta function and the Weil conjectures for non-singular curves. We derive an equation to obtain the number of solutions of equations over finite fields using Jacobi sums in order to compute the Zeta function for specific equations. Also, we introduce the necess...
- Autores:
-
Neira Lopez, Santiago
- Tipo de recurso:
- Trabajo de grado de pregrado
- Fecha de publicación:
- 2022
- Institución:
- Pontificia Universidad Javeriana
- Repositorio:
- Repositorio Universidad Javeriana
- Idioma:
- spa
- OAI Identifier:
- oai:repository.javeriana.edu.co:10554/62414
- Acceso en línea:
- http://hdl.handle.net/10554/62414
- Palabra clave:
- Weil Conjectures
Congruent Zeta function
Equations over finite fields
Gauss sum
Jacobi sum
Nonsingular Complete Curves
Divisors
Riemann-Roch Theorem
Weil Conjectures
Congruent Zeta function
Equations over finite fields
Gauss sum
Jacobi sum
Nonsingular Complete Curves
Divisors
Riemann-Roch Theorem
Matemáticas - Tesis y disertaciones académicas
Campos finitos (Álgebra)
Ecuaciones
Procesos de Gauss
- Rights
- openAccess
- License
- Atribución-NoComercial-SinDerivadas 4.0 Internacional
| Summary: | This work is a review of the congruent zeta function and the Weil conjectures for non-singular curves. We derive an equation to obtain the number of solutions of equations over finite fields using Jacobi sums in order to compute the Zeta function for specific equations. Also, we introduce the necessary algebraic concepts to prove the rationality and functionality of the zeta function. |
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